948 OPTICS LETTERS / Vol. 19, No. 13 / July 1, 1994

Grating evolution in frequency-doubling fibers

M. M. Lacerda, I. C. S. Carvalho, and W. Margulis

Pontificia Universidade Cat6lica do Rio de Janeiro, C.P. 38071, 22452-970 Rio de Janeiro, Brazil

B. Lesche

Physics Institute, Universidade Federal do Rio de Janeiro, P.O. Box 68528, Rio de Janeiro 21945-970, Brazil

Received December 3, 1993

The position and the width of the X(2) grating in a frequency-doubling fiber were studied during the preparationprocess. The peak of the grating moves several centimeters from the input end to the output end of the fiberbefore the conversion efficiency saturates. On saturation, the grating moves toward the input end and becomesnarrower.

Efficient second-harmonic generation (SHG) in Ge-doped silica-based optical fibers is known to occur af-ter a preparation process with exposure of the fiberto high-power radiation.' It is generally believedthat a periodic x(2) grating is recorded in the fiberthrough the mixing of the fundamental and second-harmonic (SH) fields, so that the phase-matching con-dition is satisfied.2 It has been speculated that theposition of the center of the grating changes duringthe preparation process and that the center movestoward the input end of the fiber. This is expected,provided that saturation prevents further growth ofthe peak while the grating continues to be recordednearer the input end. Recently, calculations withthe photovoltaic model indicate that before satura-tion is reached the grating should move away fromthe input end as preparation proceeds.3 Althoughcutback experiments could in principle reveal suchevolution, a number of different fibers would haveto be used because the measuring technique is de-structive, rendering the study tedious and imprecise.Side-light measurements, on the other hand, are non-destructive and have been used recently4 in studies ofthe length and time dependence of SHG in fibers, butthe low-amplitude signal measured with the scanningphotomultiplier from the side of the fiber is a disad-vantage in the study in detail of the early stages ofthe preparation process.

The heat-scan technique reported recently5 is aconvenient nondestructive way to study gratings infibers. The small heating element that is scannedalong the fiber causes a known shift in the phaserelationship between the fundamental and the SHfields. Through the interference between the SH sig-nal generated by the grating before and after theheating element, it is possible to infer the grating dis-tribution and determine the position of its peak. Theheating element can be sufficiently small to ensure aspatial resolution of s1 cm, and, since the signal ismeasured at the output end of the fiber (and notthrough the side), good sensitivity is obtained. Fur-thermore, since a little heat causes a significantphase shift, it is not necessary to raise the tempera-

ture near the annealing point when the conversion ef-ficiency irreversibly starts to drop, and therefore themeasurements are nondestructive. In this Letter wedescribe heat-scan studies of the time evolution of thex(2) grating in a frequency-doubling fiber.

The experiments were carried out with a Ge-dopedfiber (3 mol. %) codoped with P (0.5 wt. %) with an8.8-/ttm core diameter, An = 0.00418, and a minimumdispersion wavelength 1.299 ,um. A Nd:YAG laserwas used, operating Q switched (1.2-kHz repetitionrate) and mode locked (100 MHz), to provide for thehigh optical powers needed in self-seeded prepara-tion. A KTP crystal provided the SH light necessaryfor seeded preparation. Pieces of fiber -50 cm longwere held straight by micropositioners and preparedwith a typical IR average power of -250 mW (peakpower -40 kW). The heating element used here wasa 1.4-mm-diameter copper wire wound around and se-curely fastened to a 50-W soldering iron. The wireprotruded from the tip of the iron by 4 cm and hada small groove -0.5 mm deep and 5 mm from itsend. For the heat-scan experiments the iron was po-sitioned perpendicular to the fiber and moved alongthe bench. The fiber rested inside the little groove,and its temperature, measured with a small thermo-couple touching the wire, could be raised to -160 'C.The SH light produced was recorded with a Si photo-diode, and when necessary the signal was ampli-fied in a lock-in amplifier so that the early stagesof the preparation process were studied. The outputsignal from the lock-in amplifier was digitized andaveraged in a computer. Initially, the temperaturedependence of the phase shift was calibrated with theposition of the soldering iron kept constant.6 As thefiber's temperature was increased, the periodic be-havior of the SH signal versus the temperature wasmeasured. The period corresponded to an added 27rphase shift. Having determined that a temperaturerise of 40 K (from :22 to 62 0) corresponds to a ir shift,we carried out all subsequent heat-scan experimentswith the heating element at 62'C.

The data illustrated on a semilog scale in Fig. 1are an example of a sequence of measurements taken

0146-9592/94/130948-03$6.00/0 © 1994 Optical Society of America

July 1, 1994 / Vol. 19, No. 13 / OPTICS LETTERS 949

10000

1000

-S

cw

0a.W

100

10

1

0.10 10 20 30 40 50HEATING ELEMENT POSITION (cm)

Fig. 1. Sequence of heat-scan measurements on asemilog scale as the fiber self-prepares for SHG. Thefilled triangles indicate the power measured without theheating element before and after the scan.

with the heat scan while a fiber is self-preparedfor SHG. The total SH power was monitored asthe heating element that introduced a or phase shiftscanned the fiber at intervals as small as 5 mm. Al-though the modulation depth was not 100% (typically-50%), every measurement showed a significant dropin the region where the grating was located. Eachtrace was taken with the reading IR power equalto the power used for writing, minimizing additionalphase shifts caused by changes in the phase modu-lation of the input beam. Note, however, that thetrain of pulses of the Q-switched and mode-lockedlaser is automatically associated with a wide rangeof input powers. Consequently, the phase modula-tion varied along the train, limiting the modulationdepth recorded and leading to a finite minimum valueof P2,, even where destructive interference was great-est. The scanning time was typically 5 min, whereassignificant preparation took place on a time scale ofhours. We believe that the measurements did notinterfere with the recording of the grating.

A high-order polynomial was fitted to each setof points illustrated in Fig. 1 through a minimum-deviation procedure, and the amplitude A(z) of thegrating recorded was calculated as6

) | 2bP= az [P 2 (z) - P2. (min)] 2 |

to the various terms was chosen to reproduce the50% modulation depth observed. Equation (1) wasthen used to derive the grating shape A(z), and acomparison of this profile with the original shapeAreal(z) assumed showed that they do not differsignificantly. This result shows that the simplesubtraction of P2g, (min) makes it possible to mapthe grating profile without the detailed treatmentof the phase modulation for different powers, andFig. 2(a) shows the result of such procedure. Thesolid curves illustrate the grating amplitude profileA(z) at three different stages of the preparationprocess. One example is also given of the cor-responding experimental data obtained from theheat-scan measurement (squares) and of the polyno-mial used in Eq. (1) to derive A(z) (dashed curve).

From such measurements we found that the grat-ing moved from the input to the output end of thefiber during preparation. This can be attributed tothe fact that the SH signal builds up along the fiberlength, so that high field strengths exist further intothe fiber, and this leads to recording of the gratingaway from the input end. In the case illustrated, thecenter of the grating (Zpeak) moves from 10 cm fromthe input end for a SH average power of -8.0 nW to

1.6

1.4

in 1.2

1.0

0.8

) 0.6

E 0.4

0.2

0.0

-

-Jg

a

0

(1)

The value of P2<, (min) was subtracted from thevalues of P2., measured, because otherwise a zero inthe x(2) profile would have been introduced throughan artifact. We carried out a numerical simu-lation to verify whether this subtraction affectedthe shape of the grating. An arbitrary gratingprofile Area,(z) was chosen, and a linear phase termexp(iaz) was introduced, representing the effect ofphase modulation. The values of P2 <,(z) that shouldresult from a heat-scan measurement were thencalculated. Different input power pulses experiencedifferent phase mismatches, and the weight given

HEATING ELEMENT POSITION (cm)

(a)

0 2 4 6 8 10 12 14 16 18 20 22

HEATING ELEMENT POSITION (cm)

(b)Fig. 2. (a) Normalized grating amplitude profiles A(z) atlevels a, b, and c of Fig. 1 in a self-seeded preparation.The squares are the heat-scan data at level a, and thedashed curve is the polynomial used to derive A(z). (b)A(z) at three levels of preparation with an interruptedexternal seed.

A ooo*bo OAA )KW lp 01- ) 3A

A + ++ ++ +A C

AX XXXX,0%~~ *XX XX A

A&AA A A A AA A

Ail x ... .U a . A b

A 0_gg @O Aa

950 OPTICS LETTERS / Vol. 19, No. 13 / July 1, 1994

1-

g

24

22

20

18

18

14

12

10

8

6

4

2

0

ID.

0 0

U~~~~

0~~~~

10 100 1000 10000 100000

SH POWER (a.u.)

Fig. 3. Position of grating peak Zpeak (filled symbols) andwidth Wg (open symbols) as a function of SH power. Thesquares denote self-preparation, the circles denote inter-rupted seed preparation, and the filled triangle indicatesthe power of the seed.

20 cm for an average power of 0.50 mW. Figure 3(filled squares) illustrates the evolution Of Zpe. k, show-ing the position of the center of the x(2) grating as theSH power generated increases in self-seeded prepara-tion. For the lowest SHG power, Zpak is nearest theinput of the fiber. It can also be seen from the dataat the top of Fig. 1 and the filled squares in Fig. 3that the position of the grating center moves back inthe saturated regime. It approaches the input endof the fiber, but only slowly (:s2 cm after -6-h ex-posure to high IR power). A slight asymmetry wasalso found in most x(2) grating profiles [see Fig. 2(a)],with the leading edge being sharper than the trailingedge. The open squares in Fig. 3 show the evolu-tion of the width of the grating. The FWHM of thegrating (Wg) was found to be nearly constant at ap-proximately 10-11 cm for a wide range of SH powers.When saturation was reached, however, the value ofWg decreased to approximately 8-9 cm.

We also studied the grating evolution experimen-tally with an external SH seed signal. The averageoptical powers used for preparation were 140-mWfundamental radiation and 0.55-mW SH radiation.The profile of the grating inferred from Eq. (1) wasalways asymmetric. The width of the grating wasalways limited to the range of 2-4 cm, and through-out the preparation process its peak remained atthe input end of the fiber. We attribute this fea-ture to the fact that the seed signal used was largecompared with the SH generated by the fiber. As aconsequence, the level of SH light was always approx-imately constant along the fiber, never favoring therecording of the grating away from the input end.

We tested this interpretation by carrying out apreparation with an interrupted external seed. Av-erage optical powers of 235 mW (IR) and 14, gW (SH)were used for 1 min. After this period the gratingwas studied with the heat scan (similar IR readingpower), and subsequent preparation was carried outwith IR radiation only and no external seed. Theresults obtained are illustrated in Fig. 2(b) and bythe circles in Fig. 3. WeYfound that the grating ini-tially peaked at the input end of the fiber with an

asymmetric profile. As preparation continued andthe seed level was exceeded by the SH light gener-ated by the fiber, the peak of the grating moved awayfrom the input end, as expected. Furthermore, itsshape became more symmetric and the grating be-came wider. Near saturation the FWHM of the grat-ing was similar to that in the self-seeded case, whileZpeak was still only -10 cm from the input of the fiber,an intermediate value between those found in thecases of self-seeded and externally seeded prepara-tion. The total SH power generated in all cases wassimilar. Our findings with the heat scan were con-sistent with those of cutback measurements in thesaturated regime.

A simple numerical simulation discussed in detailelsewhere8 was carried out and showed all the mainfeatures observed with the heat scan. As the fiberwas prepared, it was found from the calculations thatparts farther from the input end experienced largerE2 ,, fields, enhancing the growth of the grating awayfrom the entrance end. When the injected SH seedwas large compared with the SH signal generatedby the fiber, the shift of the grating peak was in-hibited, as observed experimentally. Our findingsalso indicated that, under the prevailing experimen-tal conditions, self-erasure was the main saturationmechanism and was also responsible for the narrow-ing of the grating (see Fig. 3).

The results presented here show that the heat scanis a convenient and powerful technique for character-izing frequency-doubling grating in fibers. The sametechnique can be used in investigations on the phasemodulation of the grating written under high-powerexcitation as well as in studies of the time evolutionand the saturation mechanisms involved under otherlaser regimes. The heat scan can also be extended tothe study of the evolution of Bragg gratings in fibers.

It is a pleasure to thank Iakyra B. Couceiro foruseful discussions, Guy Perelmuter for computationalassistance, and the Ericsson Network Research Cen-ter (formerly Ericsson Cables) for providing the fiberused in this study. The financial support of theConselho Nacional de Pesquisa and of Telebrds isgratefully acknowledged.

References

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